I was reading about Cauchy-Goursat theorem and one step in the proof stumped me. It's the easier one, that is, Cauchy's proof that requires the complex valued function f be analytic in R, and f' to be continuous throughout the region R interior to and on some simple closed contour C. So that the...
I have a question about complex valued functions, say f(z) where z=x+iy is a complex variable.
Can every such complex valued function be represented by:
f(z)=u(x,y)+iv(x,y)?
Also, is the limit of the conjugate such a function equal to the conjugate of the limit of the function?
Something like...
Hello, I was looking at Riley's solution manual for this specific problem. Along the way, he ended up with a quadratic inequality:
If you looked at the image, he said it is given that λ is real, but he asserted that λ has no real roots because of the inequality. Doesn't that mean λ is...
I have been restudying vector calculus, especially on topics pertaining to line integrals, surface integrals (and the accompanying vector forms). One problem I have encountered from the book I have been using is that it seems there are some theorems and results that are only restricted to...
Let's say I have a matrix M such that for vectors R and r in xy-coordinate system:
R=Mr
Suppose we diagonalized it so that there is another matrix D such that for vectors R' (which is also R) and r' (which is also r) in x'y'-coordinate system:
R'=Dr'
D is a matrix with zero elements except for...
For the series such that: \Sigma _{n=1} ^{\infty} a_n =\Sigma _{n=1} ^{\infty} b_n A certain theorem says that these series are equal even if a_n = b_n only for n>m. That is, even if two infinite series differ for a finite number of terms, it will still converge for the same sum. I am thinking...
I have a question about limits at infinity, particularly, about a limit I have seen in the context of infinite series convergence.
Let's say we have an infinite series where the the sequence of partial sums is given by {S(n)} and also, it is convergent and the sum is equal to S. Then we know...
From the elementary texts, dispersion is the phenomenon where the refractive index of a medium depends on the wavelength of electromagnetic radiation through it. From what I've read, it is the wavelength of the radiation in vacuum. Also, it is said that the refractive index increases with...
Suppose I have a vector V and I want to compute for the line integral from point (1,1,0) to point (2,2,0) and I take the path of the least distance (one that traces the identity function).
The line integral is of the form:
\int _a ^b \vec{V} \cdot d\vec{l}
Where:
x=y, \ d\vec{l}...
Does a di/dt<0 mean an increasing current moving from a lower potential to a higher potential (if we define the direction of current to be the flow of the positive charges)? Similar question with negative current i.e.; dq/dt<0.
Is power a quantity defined by:
\frac{dU}{dt} and \frac{dW}{dt}
Is it just defined to be it, or can it be derived in terms of the other (I mean, dU/dt in terms of dW/dt and vice versa)?
I now there's physical motivation to it, but sometimes I just can't help trying to ponder how these equations...
En and Ec are the non-conservative and conservative electric field respectively.
I've quoted this from the textbook I'm using (University Physics by Young and Freedman 12th edition).
Now, it seems to me that the author just invoked the assumption that the inductor have negligible resistance...
I'm kind of new to proof based mathematics, can you guys give me an advice on what a good book pertaining to this should I get?
I don't really care about what particular subject in mathematics it is, just as long as it can give me a good knowledge and skills in proving, and it's something...
I found myself having a hard time choosing what mathematical physics text should I stick with. I'd like to think of myself as mathematically inclined, and I would really prefer a mathematical physics book that emphasizes 'the maths' and the proofs and not just the methods while maintaining its...
By rolled, I mean this kind of basic homemade capacitors:
http://www.ehow.com/how-does_4852927_building-a-capacitor.html
Kind sirs, I have few questions regarding this kind of capacitor:
1.) Would I still be able to get the 'theoretical free-space' capacitor of the same dimensions using C_o =...
I want to make a parallel plate capacitor without dielectric between it, that is, a capacitor with free space.
Can I do a working capacitor with just a two parallel cardboard coated in aluminum? I figured it should look like this:
Also, if there's anyone who's got a better idea on how I...
I just had a really pressing semester, it was quite horrible actually. I still managed to get a good grade and now we're on break.
Do I take a break or do I study? What I mean by break is that, I'm thinking of doing nothing related to physics or mathematics (academics) and loosen myself up...
I'm sure there are some of you (most, if not) who've experienced this, but mine's really bad. When I have classes for the next day, I could not sleep the night before because I'm thinking too much, ironically it's about being not able to sleep.
During the days where I have no classes, I seem...
It's just a simple question about the pressure under and over the plane's wing problem that I'm trying to answer. Well, actually I've already answered it, but one just keeps bugging me. Why don't we consider the difference in altitude of the lower and upper points of the fluid (air) when we use...
I'm having a little problem with my book as I was reading about fluid mechanics. The book seems to have skipped a bit of some crucial part (at least for me) during the derivation for fluid pressure at certain depths (where the weight of the fluid is not neglected).
Here, I'll try to reconstruct...
I'm a physics major a bit of inclination to mathematics. The semester just ended, and I didn't particularly have a bad one. It's just I had a really mediocre grade after the semester, I'm a bit disappointed since while I'm busy reading through the proofs it seems it didn't really do me much good...
It's been a while since I've done any work-energy questions, and I just noticed how vague some questions could be (or maybe I don't understand it that well). Anyway, suppose I have a box moving down an incline where the only forces acting on it are its weight, the normal force, and friction...
As the thread title says I'm interested in Chaos Theory, Complex Systems, and Nonlinear Systems. If I can help it, I'd like to study these at graduate level. My question is what kind and how much mathematics I'm supposed to know if I'm to study these?
I've taken a liking to studying mathematics, though I'm a physics major I've always tried to learn things as rigorous as possible whether it's mathematics or physics. Now, I haven't quite gotten to the level where I just breeze through proofs or at least when I study the theorems it still takes...
I'm not sure if this should go here, anyway I'm contemplating over what Calculus text book should I buy. Textbooks that are sold locally are somewhat limited to our country so I only have 2 'good' books to choose from. It's either Leithold's or Stewart's, I don't know which one of these are...
When I study mathematics, I just do it leisurely and at my own pace. Over the course of my whole mathematics education, I've enjoyed learning the abstract ideas/concept in it, the problem is I'm a bit clumsy doing calculations. I can study and do proofs/concepts but practicing problem sets eats...
I actually came from another department in my college before doing physics and I know pretty well that physics requires more work than my previous major. Now, how does one keep himself motivated? Though, I can say that I'm pretty much motivated in doing science and mathematics but there would be...
This is my first post and I've decided to make a thread right away. I just want to ask about how should I work on my maths?
Not so long ago I flunked one mathematics quiz, I don't know if it's because I'm not studying hard enough or if it's because of my careless mistakes or if it's plain...